Question: Solve for $x$ and $y$ using elimination. ${-3x-4y = -45}$ ${5x+5y = 60}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${-15x-20y = -225}$ $15x+15y = 180$ Add the top and bottom equations together. $-5y = -45$ $\dfrac{-5y}{{-5}} = \dfrac{-45}{{-5}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x-4y = -45}\thinspace$ to find $x$ ${-3x - 4}{(9)}{= -45}$ $-3x-36 = -45$ $-3x-36{+36} = -45{+36}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 9}$ into $\thinspace {5x+5y = 60}\thinspace$ and get the same answer for $x$ : ${5x + 5}{(9)}{= 60}$ ${x = 3}$